I think the obsession with Brogdon has to do with the fact that he checks a lot of boxes. Ideally, we want a point guard who can run an offense, but can be effective off the ball as well, since Booker is going to have the ball in his hands most of the time. He should be a good defender, and a good three point shooter.
I don't think it's necessarily about Brogdon. It's about anyone who can be competent at running an offense, great on defense, and very good three-point shooter. Guys like Brogdon and Holiday check all those boxes. When you get to guys like Rubio, Collison, etc, you have to start compromising. Rubio can't shoot, Collison apparently is not as good of a defender as I thought he was watching him a few times, etc. Hell, even some of the top-tier PGs don't check some boxes. Russell is not good defensively, neither is Kyrie, neither is Walker. Walker, Conley, etc may not be effective off the ball.